The research presented in this thesis addresses general forms of real and symmetric n×n matrices M, C and K for an inverse quadratic eigenvalue problem (IQEP), Q(?)x=(?^2 M+?C+K)x=0, so that Q(?) has a prescribed set of non- simple eigenvalues. It is shown that this inverse problem involves certain free parameters. Via appropriate choice of free variables in the general form of IQEP, we solve an IQEP with non- simple eigenvalues, and so, we present a numerical model for updating QEPs which produces the mass, damping and stiffness matrices. To this end the complete set of eigenpaires will be employed.